Hawk's agent Mike McCartney told the website the long-haired linebacker had signed Green Bay's 2006 first-round draft pick (number five overall), one day after the team released him in a cost-saving move.
Details of the deal with Hawk, who was scheduled to earn $10.5 million in 2011, were not released.
A freeze on any NFL business could come at midnight Thursday when the collective bargaining agreement between NFL owners and the NFL Players Association was set to expire.
Also taking care of some roster concerns was the New York Giants, who ensured competition in their return game when they announced that Domenik Hixon and Darius Reynaud had signed contract extensions.
Hixon, entering his sixth NFL season and fifth with the Giants, missed the entire 2010 season after tearing a knee ligament during a preseason practice.
Reynaud is entering his fourth NFL season and second with the Giants. He and backup quarterback Sage Rosenfels were acquired in a trade with the Minnesota Vikings just before the start of the 2010 season.
(Reporting by Larry Fine, Editing by Steve Ginsburg)